Robust Timing of Markdowns

We propose an approach to the timing of markdowns over a finite time horizon that does not require the precise knowledge of the underlying probabilities, instead relying on range forecasts for the arrival rates of the demand processes, and that captures the degree of the manager’s risk aversion through intuitive budget-of-uncertainty functions. These budget functions … Read more

Robust Unit Commitment Problem with Demand Response and Wind Energy

To improve the efficiency in power generation and to reduce the greenhouse gas emission, both Demand Response (DR) strategy and intermittent renewable energy have been proposed or applied in electric power systems. However, the uncertainty and the generation pattern in wind farms and the complexity of demand side management pose huge challenges in power system … Read more

Two-Stage Robust Power Grid Optimization Problem

Under the deregulated energy market environment, plus the integration of renewable energy generation, both the supply and demand of a power grid system are volatile and under uncertainty. Accordingly, a large amount of spinning reserve is required at each bus to maintain the reliability of the power grid system in the traditional approach. In this … Read more

Robust and Stochastically Weighted Multi-Objective Optimization Models and Reformulations

In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce … Read more

Energy Security: a robust optimization approach to design a robust European energy supply via TIAM

Energy supply routes to a given TIAM region (say E.U.) are subject to randomness, resulting in partial or total closure of a route (corridor). For instance: a pipeline may be subject to technical problems that reduce its capacity. Or, oil supply by tanker may be reduced for political reasons or because of equipment mishaps at … Read more

Robust capacity expansion solutions for telecommunication networks with uncertain demands

We consider the capacity planning of telecommunication networks with linear investment costs and uncertain future traffic demands. Transmission capacities must be large enough to meet, with a high quality of service, the range of possible demands, after adequate routings of messages on the created network. We use the robust optimization methodology to balance the need … Read more

Distributionally Robust Joint Chance Constraints with Second-Order Moment Information

We develop tractable semidefinite programming (SDP) based approximations for distributionally robust individual and joint chance constraints, assuming that only the first- and second-order moments as well as the support of the uncertain parameters are given. It is known that robust chance constraints can be conservatively approximated by Worst-Case Conditional Value-at-Risk (CVaR) constraints. We first prove … Read more

Generalized Decision Rule Approximations for Stochastic Programming via Liftings

Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations … Read more

Bilevel Derivative-Free Optimization and its Application to Robust Optimization

We address bilevel programming problems when the derivatives of both the upper and the lower level objective functions are unavailable. The core algorithms used for both levels are trust-region interpolation-based methods, using minimum Frobenius norm quadratic models when the number of points is smaller than the number of basis components. We take advantage of the … Read more